Why is my rendered my image not being saved as a file?
Have you actually saved it ?

Blender does the render and displays it but doesn't automatically save it as an image.

To save it, use the top left of your Image Viewer window click on "Image" > "Save As" and give your file a name and save it.

In 2.8



in 2.79 use the UV/Image editor window



If you want to save the render automatically you need to render as animation (CtrlF12), just set the range to render only one frame.

Do a little more research and/or show that you have done some research next time you want to ask something here. Some folks on this forum don't have quite as much patience as I do and might reject your question for showing too little (if any) previous research